# Re: Derivative via mathematica

• To: mathgroup@smc.vnet.net
• Subject: [mg10533] Re: [mg10486] Derivative via mathematica
• From: Bob Hanlon <BobHanlon@aol.com>
• Date: Tue, 20 Jan 1998 02:23:19 -0500
• Organization: AOL (http://www.aol.com)

```f[t_, m_, b_] := m/(1+Exp[1/t] +b)

m/: Dt[m, t] = p;
b/: Dt[b, t] = q;

D[f[t, m[t], b[t]], t]

\!\(\*
RowBox[{
RowBox[{"-",
FractionBox[
RowBox[{\(m[t]\), " ",
RowBox[{"(",
RowBox[{\(-\(E\^\(1\/t\)\/t\^2\)\), "+",
RowBox[{
SuperscriptBox["b", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}]}], ")"}]}],
\(\((1 + E\^\(1\/t\) + b[t])\)\^2\)]}], "+",
FractionBox[
RowBox[{
SuperscriptBox["m", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
\(1 + E\^\(1\/t\) + b[t]\)]}]\)

Dt[f[t, m, b], t]

\!\(p\/\(1 + b + E\^\(1\/t\)\) -
\(m\ \((q - E\^\(1\/t\)\/t\^2)\)\)\/\((1 + b + E\^\(1\/t\))\)\^2\)

Bob Hanlon

```

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